Kasich, Portman, and Thune seem a bit too safe, though would be good. Graham and Sandoval would be interesting, if it weren't for the Base not feeling so sure with Rice. Trump, Walker, Rubio, and Paul would be good on paper, but would probably be a liability for the Ticket. Cotton, Daniels, and McMorris Rodgers would be my finalists.
As for the Wild Cards? Christie would serve better as AG. Baker is good where he is. Stick a fork in Perry and Bloomberg. Bryant and Faulconer would be interesting, but there are better choices. Webb would be good for the VA Secretary. Dan Bane would be worth looking into, though I doubt he'd be able to make it into the final few. Gardner would be my pick of the wild cards.
Either way, this has been a great timeline, Progressive! I'd like to see what the Rice Administration would look like, if you were were thinking of having it go that far that is. Keep up the good work.